Question

look at this set of ordered pairs:
(12, -11)
(8, -13)
(8, 0)
(-18, -11)
which mapping diagram represents this relation?

Explanation:

Step1: Identify domain and range values

The domain consists of the x - values of the ordered pairs: \(12\), \(8\), \(8\), \(- 18\). So the unique domain values are \(-18\), \(8\), \(12\).
The range consists of the y - values of the ordered pairs: \(-11\), \(-13\), \(0\), \(-11\). So the unique range values are \(-13\), \(-11\), \(0\).

Step2: Analyze mappings for each domain value

• For \(x = 12\) (from \((12,-11)\)), it maps to \(y=-11\).
• For \(x = 8\): from \((8, - 13)\) it maps to \(y = - 13\) and from \((8,0)\) it maps to \(y = 0\).
• For \(x=-18\) (from \((-18,-11)\)), it maps to \(y=-11\).

Now let's check the two mapping diagrams:

• First diagram:
• \(-18\) maps to \(-11\) (correct as per \((-18,-11)\)).
• \(8\) maps to \(-13\) (from \((8, - 13)\)) and \(8\) maps to \(0\) (from \((8,0)\)) (correct).
• \(12\) maps to \(-11\) (from \((12,-11)\)) (correct).
• Second diagram:
• The mapping for \(8\) does not include mapping to \(-13\) and \(0\) correctly (since in the second diagram, the connections for \(8\) do not match the ordered pairs \((8, - 13)\) and \((8,0)\)).

Answer:

The first mapping diagram (with Domain \(-18\), \(8\), \(12\) and Range \(-13\), \(-11\), \(0\) where \(-18\) maps to \(-11\), \(8\) maps to \(-13\) and \(0\), and \(12\) maps to \(-11\))